3. Vectors

Draw each of the following vectors, label an angle that specifies the vector's direction, and then find the vector's magnitude and direction. A = 3.0i + 7.0j

A velocity vector 40 degrees below the positive x-axis has a y-component of -10 m/s. What is the value of its x-component?

Draw each of the following vectors, label an angle that specifies the vector's direction, and then find the vector's magnitude and direction. v = (14i - 11j) m/s

The bacterium E. coli is a single-cell organism that lives in the gut of healthy animals, including humans. When grown in a uniform medium in the laboratory, these bacteria swim along zig-zag paths at a constant speed of 20 μm/s. FIGURE P3.42 shows the trajectory of an E. coli as it moves from point A to point E. What are the magnitude and direction of the bacterium's average velocity for the entire trip?

A postal employee drives a delivery truck over the route shown in Fig. E1.25. Use the method of components to determine the magnitude and direction of her resultant displacement. In a vector-addition diagram (roughly to scale), show that the resultant displacement found from your diagram is in qualitative agreement with the result you obtained by using the method of components.

For the vectors A and B in Fig. E1.24 use the method of components to find the magnitude and direction of the vector difference B - A

Four forces are exerted on the object shown in FIGURE $P3.45$. (Forces are measured in newtons, abbreviated $\text{N}$.) The net force on the object is ${\vec{F}}_{\text{net}}={\vec{F}}_1+{\vec{F}}_2+{\vec{F}}_3+{\vec{F}}_4=4.0\hat{i}\text{N}$. What are (a) ${\vec{F}}_3$ and (b) ${\vec{F}}_4$? Give your answers in component form.

For the vectors A and B in Fig. E1.24 use the method of components to find the magnitude and direction of the vector sum A + B

Draw each of the following vectors, label an angle that specifies the vector's direction, then find its magnitude and direction. r = (-2.0i - 1.0j) cm

While vacationing in the mountains you do some hiking. In the morning, your displacement is $S_{morning}=(2000\text{m},\text{east})+(3000\text{m},\text{north})+(200\text{m},\text{vertical})$. Continuing on after lunch, your displacement is $S_{afternoon}=(1500\text{m},\text{west})+(2000\text{m},\text{north})-(300\text{m},\text{vertical})$. At the end of the hike, how much higher or lower are you compared to your starting point?

Let A = 4i - 2j, B = -3i + 5j, and F = A - 4B. Write vector F in component form.

FIGURE P3.26 shows vectors A and B. Find D = 2A ＋B Write your answer in component form.

Let A = 4i - 2j, B = -3i + 5j, and C = A + B. Write vector C in component form.

For the vectors A and B in Fig. E1.24 use the method of components to find the magnitude and direction of the vector difference A - B

Use components to determine the magnitude and direction of G = E＋F.